`(dy)/(dx)=(1)/(sin x)+e^(x)`

Ify,=sqrt(((1+cos x)/(2))), provethat (dy)/(dx)=-(1)/(2)(sin x)/(2) If y,=sqrt((1+sin x)/(1-sin x)), prove that cos x(dy)/(dx)=y

Solve: (dy)/(dx)=(1)/(sin^(4)x+cos^(4)x) (ii) (dy)/(dx)=(3e^(2x)+3e^(4x))/(e^(x)+e^(-x))

(dy)/(dx)=e^(-y)*sin x+e^((x-y))

(dy)/(dx)=e^(-y)sin x+e^((x-y))

solve (dy)/(dx)=e^(-y)*sin x+e^((x-y))

(dy)/(dx)=(e^(2x)+1)/(e^(x))

(dy) / (dx) = (sin x) / (e ^ (y))

The solution of (dy)/(dx)=e^(x)(sin x + cos x) is

If y = f(x) and x = g(y), where g is the inverse of f, i.e., g = f^(-1) and if (dy)/(dx) and (dx)/(dy) both exist and (dx)/(dy) ne 0 , show that (dy)/(dx) = (1)/((dx//dy)) . Hence, (1) find (d)/(dx) (tan^(-1)x) (2) If y=sin^(-1)x, -1lexle1, -(pi)/(2)leyle(pi)/(2) , then show that (dy)/(dx)=(1)/(sqrt(1-x^(2))) where |x| lt 1 .

The solution of (dy)/(dx)=e^(x)(sin^(2)x+sin2x)/(y(2log y+1)) is